Question

similar figures and area quick check
use the image to answer the question.
chaz draws a square with sides equal to 4 units, then he dilates the square so the sides are equal to 6 units. chaz writes a fraction in lowest terms to express the relationship between the area of the original square and the dilated square, with the numerator expressing the area of the dilated square. what is that fraction?
(1 point)
\\( 2\frac{1}{4} \\)
\\( \frac{2}{3} \\)
\\( \frac{4}{9} \\)
\\( \frac{16}{36} \\)

Explanation:

Step1: Calculate area of original square

The formula for the area of a square is \( A = s^2 \), where \( s \) is the side length. For the original square with \( s = 4 \) units, the area \( A_{original} = 4^2 = 16 \) square units.

Step2: Calculate area of dilated square

For the dilated square with \( s = 6 \) units, using the same area formula, the area \( A_{dilated} = 6^2 = 36 \) square units.

Step3: Find the fraction

The fraction is \( \frac{A_{dilated}}{A_{original}}=\frac{36}{16} \). Simplify this fraction by dividing both numerator and denominator by their greatest common divisor, which is 4. So, \( \frac{36\div4}{16\div4}=\frac{9}{4}=2\frac{1}{4} \). Wait, no, wait. Wait, the problem says "the numerator expressing the area of the dilated square" and we need the fraction of dilated over original? Wait, no, wait the options: let's check again. Wait, original area is 16, dilated is 36. So the fraction is \( \frac{36}{16} \)? No, wait no, wait the options have \( \frac{36}{16} \) simplified? Wait no, wait the options: the last option is \( \frac{16}{36} \)? No, wait no, I think I messed up. Wait, original area is 16, dilated is 36. So the fraction with numerator as dilated area is \( \frac{36}{16} \), but simplified, divide numerator and denominator by 4: \( \frac{9}{4} = 2\frac{1}{4} \), which is the first option. Wait, let's recheck:

Original square: side 4, area \( 4\times4 = 16 \).

Dilated square: side 6, area \( 6\times6 = 36 \).

Fraction: \( \frac{\text{dilated area}}{\text{original area}} = \frac{36}{16} = \frac{9}{4} = 2\frac{1}{4} \), which is the first option.

Answer:

A. \( 2\frac{1}{4} \)